Thus, \(ab\) -plane ordering in the A-type AFM state of EuMg\(_2\) Bi\(_2\)  is favored over \(c\) -axis ordering associated with magnetic-dipole interactions, as observed. This is consistent with the critical fields \(H^{\rm c}\)  at \(T=1.8\)  K obtained from \(M(H)\)  isotherms \(H_c^{\rm c}= 40(3)\)  kOe and \(H_{ab}^{\rm c}= 27.5(2)\)  kOe [1]}, yielding \(H_c^{\rm c}- H_{ab}^{\rm c}\approx 12,000\)  Oe. This is because it is easier to cant the moments in each domain towards an \(ab\) -plane field than it is to cant them along the \(c\)  axis according to Eqs. (REF ). On the other hand, this difference in critical fields is significantly larger than the magnitude of \(\Delta H\)  in Eq. (REF ), suggesting the presence of a source of \(\Delta H\)  in addition to the magnetic-dipole interaction.
